Surviving an avalanche of data

Open the sports or business section of your daily newspaper, and you are immediately bombarded with an array of graphs, tables, diagrams, and statistical reports that require interpretation. Across all walks of life, the need to understand statistics is fundamental. Given that our youngsters’ future world will be increasingly data laden, scaffolding their statistical understanding and reasoning is imperative, from the early grades on. The National Council of Teachers of Mathematics (NCTM) continues to emphasize the importance of early statistical learning; data analysis and probability was the Council’s professional development “Focus of the Year” for 2007–2008. We need such a focus, especially given the results of the statistics items from the 2003 NAEP. As Shaughnessy (2007) noted, students’ performance was weak on more complex items involving interpretation or application of items of information in graphs and tables. Furthermore, little or no gains were made between the 2000 NAEP and the 2003 NAEP studies. One approach I have taken to promote young children’s statistical reasoning is through data modeling. Having implemented in grades 3 –9 a number of model-eliciting activities involving working with data (e.g., English 2010), I observed how competently children could create their own mathematical ideas and representations—before being instructed how to do so. I thus wished to introduce data-modeling activities to younger children, confi dent that they would likewise generate their own mathematics. I recently implemented data-modeling activities in a cohort of three first-grade classrooms of six year- olds. I report on some of the children’s responses and discuss the components of data modeling the children engaged in.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.